aboutsummaryrefslogtreecommitdiffhomepage
path: root/Eigen/src/Core/StableNorm.h
blob: be04ed44d8f4f322aa1a05e8376f4f63a7f1fc91 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_STABLENORM_H
#define EIGEN_STABLENORM_H

namespace Eigen { 

namespace internal {

template<typename ExpressionType, typename Scalar>
inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& scale, Scalar& invScale)
{
  Scalar maxCoeff = bl.cwiseAbs().maxCoeff();
  
  if(maxCoeff>scale)
  {
    ssq = ssq * numext::abs2(scale/maxCoeff);
    Scalar tmp = Scalar(1)/maxCoeff;
    if(tmp > NumTraits<Scalar>::highest())
    {
      invScale = NumTraits<Scalar>::highest();
      scale = Scalar(1)/invScale;
    }
    else if(maxCoeff>NumTraits<Scalar>::highest()) // we got a INF
    {
      invScale = Scalar(1);
      scale = maxCoeff;
    }
    else
    {
      scale = maxCoeff;
      invScale = tmp;
    }
  }
  else if(maxCoeff!=maxCoeff) // we got a NaN
  {
    scale = maxCoeff;
  }
  
  // TODO if the maxCoeff is much much smaller than the current scale,
  // then we can neglect this sub vector
  if(scale>Scalar(0)) // if scale==0, then bl is 0 
    ssq += (bl*invScale).squaredNorm();
}

template<typename Derived>
inline typename NumTraits<typename traits<Derived>::Scalar>::Real
blueNorm_impl(const EigenBase<Derived>& _vec)
{
  typedef typename Derived::RealScalar RealScalar;  
  using std::pow;
  using std::sqrt;
  using std::abs;
  const Derived& vec(_vec.derived());
  static bool initialized = false;
  static RealScalar b1, b2, s1m, s2m, rbig, relerr;
  if(!initialized)
  {
    int ibeta, it, iemin, iemax, iexp;
    RealScalar eps;
    // This program calculates the machine-dependent constants
    // bl, b2, slm, s2m, relerr overfl
    // from the "basic" machine-dependent numbers
    // nbig, ibeta, it, iemin, iemax, rbig.
    // The following define the basic machine-dependent constants.
    // For portability, the PORT subprograms "ilmaeh" and "rlmach"
    // are used. For any specific computer, each of the assignment
    // statements can be replaced
    ibeta = std::numeric_limits<RealScalar>::radix;                 // base for floating-point numbers
    it    = std::numeric_limits<RealScalar>::digits;                // number of base-beta digits in mantissa
    iemin = std::numeric_limits<RealScalar>::min_exponent;          // minimum exponent
    iemax = std::numeric_limits<RealScalar>::max_exponent;          // maximum exponent
    rbig  = (std::numeric_limits<RealScalar>::max)();               // largest floating-point number

    iexp  = -((1-iemin)/2);
    b1    = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // lower boundary of midrange
    iexp  = (iemax + 1 - it)/2;
    b2    = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // upper boundary of midrange

    iexp  = (2-iemin)/2;
    s1m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // scaling factor for lower range
    iexp  = - ((iemax+it)/2);
    s2m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // scaling factor for upper range

    eps     = RealScalar(pow(double(ibeta), 1-it));
    relerr  = sqrt(eps);                                            // tolerance for neglecting asml
    initialized = true;
  }
  Index n = vec.size();
  RealScalar ab2 = b2 / RealScalar(n);
  RealScalar asml = RealScalar(0);
  RealScalar amed = RealScalar(0);
  RealScalar abig = RealScalar(0);
  for(typename Derived::InnerIterator it(vec, 0); it; ++it)
  {
    RealScalar ax = abs(it.value());
    if(ax > ab2)     abig += numext::abs2(ax*s2m);
    else if(ax < b1) asml += numext::abs2(ax*s1m);
    else             amed += numext::abs2(ax);
  }
  if(amed!=amed)
    return amed;  // we got a NaN
  if(abig > RealScalar(0))
  {
    abig = sqrt(abig);
    if(abig > rbig) // overflow, or *this contains INF values
      return abig;  // return INF
    if(amed > RealScalar(0))
    {
      abig = abig/s2m;
      amed = sqrt(amed);
    }
    else
      return abig/s2m;
  }
  else if(asml > RealScalar(0))
  {
    if (amed > RealScalar(0))
    {
      abig = sqrt(amed);
      amed = sqrt(asml) / s1m;
    }
    else
      return sqrt(asml)/s1m;
  }
  else
    return sqrt(amed);
  asml = numext::mini(abig, amed);
  abig = numext::maxi(abig, amed);
  if(asml <= abig*relerr)
    return abig;
  else
    return abig * sqrt(RealScalar(1) + numext::abs2(asml/abig));
}

} // end namespace internal

/** \returns the \em l2 norm of \c *this avoiding underflow and overflow.
  * This version use a blockwise two passes algorithm:
  *  1 - find the absolute largest coefficient \c s
  *  2 - compute \f$ s \Vert \frac{*this}{s} \Vert \f$ in a standard way
  *
  * For architecture/scalar types supporting vectorization, this version
  * is faster than blueNorm(). Otherwise the blueNorm() is much faster.
  *
  * \sa norm(), blueNorm(), hypotNorm()
  */
template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::stableNorm() const
{
  using std::sqrt;
  using std::abs;
  const Index blockSize = 4096;
  RealScalar scale(0);
  RealScalar invScale(1);
  RealScalar ssq(0); // sum of square
  
  typedef typename internal::nested_eval<Derived,2>::type DerivedCopy;
  typedef typename internal::remove_all<DerivedCopy>::type DerivedCopyClean;
  DerivedCopy copy(derived());
  
  enum {
    CanAlign = (   (int(DerivedCopyClean::Flags)&DirectAccessBit)
                || (int(internal::evaluator<DerivedCopyClean>::Alignment)>0) // FIXME Alignment)>0 might not be enough
               ) && (blockSize*sizeof(Scalar)*2<EIGEN_STACK_ALLOCATION_LIMIT)
                 && (EIGEN_MAX_STATIC_ALIGN_BYTES>0) // if we cannot allocate on the stack, then let's not bother about this optimization
  };
  typedef typename internal::conditional<CanAlign, Ref<const Matrix<Scalar,Dynamic,1,0,blockSize,1>, internal::evaluator<DerivedCopyClean>::Alignment>,
                                                   typename DerivedCopyClean::ConstSegmentReturnType>::type SegmentWrapper;
  Index n = size();
  
  if(n==1)
    return abs(this->coeff(0));
  
  Index bi = internal::first_default_aligned(copy);
  if (bi>0)
    internal::stable_norm_kernel(copy.head(bi), ssq, scale, invScale);
  for (; bi<n; bi+=blockSize)
    internal::stable_norm_kernel(SegmentWrapper(copy.segment(bi,numext::mini(blockSize, n - bi))), ssq, scale, invScale);
  return scale * sqrt(ssq);
}

/** \returns the \em l2 norm of \c *this using the Blue's algorithm.
  * A Portable Fortran Program to Find the Euclidean Norm of a Vector,
  * ACM TOMS, Vol 4, Issue 1, 1978.
  *
  * For architecture/scalar types without vectorization, this version
  * is much faster than stableNorm(). Otherwise the stableNorm() is faster.
  *
  * \sa norm(), stableNorm(), hypotNorm()
  */
template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::blueNorm() const
{
  return internal::blueNorm_impl(*this);
}

/** \returns the \em l2 norm of \c *this avoiding undeflow and overflow.
  * This version use a concatenation of hypot() calls, and it is very slow.
  *
  * \sa norm(), stableNorm()
  */
template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::hypotNorm() const
{
  return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());
}

} // end namespace Eigen

#endif // EIGEN_STABLENORM_H